The theory of nonnegative matrices is an example of a theory motivated in its origins and development by purely mathematical concerns that later proved to have a remarkably broad spectrum of applications to such diverse fields as probability theory, numerical analysis, economics, dynamical programming, and demography. At the heart of the theory is what is usually known as the Perron–Frobenius Theorem. It was inspired by a theorem of Oskar Perron on positive matrices, usually called Perron’s Theorem. This paper is primarily (...) concerned with the origins of Perron’s Theorem in his masterful work on ordinary and generalized continued fractions (1907) and its role in inspiring the remarkable work of Frobenius on nonnegative matrices (1912) that produced, inter alia, the Perron–Frobenius Theorem. The paper is not at all intended exclusively for readers with expertise in the theory of nonnegative matrices. Anyone with a basic grounding in linear algebra should be able to read this article and come away with a good understanding of the Perron–Frobenius Theorem as well as its historical origins. The final section of the paper considers the first major application of the Perron–Frobenius Theorem, namely, to the theory of Markov chains. When he introduced the eponymous chains in 1908, Markov adumbrated several key notions and results of the Perron–Frobenius theory albeit within the much simpler context of stochastic matrices; but it was by means of Frobenius’ 1912 paper that the linear algebraic foundations of Markov’s theory for nonpositive stochastic matrices were first established by R. Von Mises and V.I. Romanovsky. (shrink)

Graphical AbstractScience and technology consortia provide a viable solution for the recent unsustainable academic growth in biomedical research.

In this article I explore various facets of Nozick’s famous thought experiment involving the experience machine. Nozick’s original target is hedonism—the view that the only intrinsic prudential value is pleasure. But the argument, if successful, undermines any experientialist theory, i.e. any theory that limits intrinsic prudential value to mental states. I first highlight problems arising from the way Nozick sets up the thought experiment. He asks us to imagine choosing whether or not to enter the machine and uses our choice (...) (or rather the choice he assumes most people will have) as evidence against experientialist theories. But for this strategy to succeed it must be possible to distinguish between self-interested and non-self-interested reasons for declining to enter the machine, and there is no obvious way to do this without begging the question against the hedonist. In successive sections I then (a) consider a common misconception of Nozick’s conclusion (that he thinks machine life is the worst life), (b) consider different intuitions about what is important to well-being but missing from machine life, and finally (c) explain what “the experience requirement” is, and describe its relationship to debates about experientialist theories. (shrink)

The literature of economic theory, like that of philosophy, abounds in prefaces and prolegomena. Methodology and analysis of concepts take an important place in a science which has not found the sure path of development. But there is no sure path for methodology either. The selfconscious methodology of social science has been largely a borrowing from that of physical science, where procedures have developed to a stage of considerable maturity. But the analogy falls down where guidance is most needed, at (...) the points where social science is most likely to develop new concepts and new types of structure. Philosophers have not been lacking, indeed, to belittle the entire enterprise, and to deny the possibility of anything that could strictly be called social science. (shrink)

Decision-Making Capacity First published Tue Jan 15, 2008; substantive revision Fri Aug 14, 2020 In many Western jurisdictions the law presumes that adult persons, and sometimes children that meet certain criteria, are capable of making their own medical decisions; for example, consenting to a particular medical treatment, or consenting to participate in a research trial. But what exactly does it mean to say that a subject has or lacks the requisite capacity to decide? This question has to do with what (...) is commonly called “decisional capacity”, a central concept in health care law and ethics, and increasingly an independent topic of philosophical inquiry. -/- Decisional capacity can be defined as the ability of subjects to make their own medical decisions. Somewhat similar questions of capacity arise in other contexts, such as capacity to stand trial in a court of law and the ability to make decisions that relate to personal care and finances. However, the history behind the more general legal notions of capacity to stand trial and capacity to manage one’s life is different and operates somewhat differently in law (Roth, Meisel, & Litz 1977; Zapf & Roesch 2005). For the purposes of this discussion the notion of decisional capacity will be limited to medical contexts only; most notably, those where decisions to consent or to refuse treatment or participation in clinical research are concerned. (shrink)

There is a strong appetite in ‘the wild’ (i.e., beyond the academy) for public philosophy. There are myriad forums available, from magazines and online publications to podcasts and YouTube videos, for those who wish to engage in philosophy in a non-academic context. For academic philosophers, this has raised methodological and metaphilosophical questions like: ‘what is the best way to engage in public philosophy?’ and ‘what are our aims when we engage in public philosophy?’ But what do ‘the public’ want? If (...) public philosophy is philosophy written for a public audience, what is it, exactly, that it can or might do for them? Several answers have been proposed by philosophers, but less attention has been paid to how the public themselves might answer that question. The aim of this essay is to try and put together at least the beginning of an answer. In June 2022 we put out a survey in the hope of eliciting views from ‘the public’ on issues relating to the nature and aims of both philosophy (more generally) and public philosophy. In doing so, our aim was to take a ‘democratic’ approach to answering the question: What is public philosophy? (shrink)

This paper considers two conceptual expansions of Du Boisian double consciousness—white double consciousness (Alcoff 2015) and kaleidoscopic consciousness (Medina 2013)—both of which aim to articulate the moral-epistemic potential of cultivating double consciousness from racially dominant or other socially privileged positions. We analyze these concepts and challenge them on the grounds that they lack continuity with their Du Boisian predecessor and face problems of practical feasibility. As we show, these expansions obscure structural barriers that make white double consciousness and kaleidoscopic consciousness (...) unlikely antidotes to the kind of racial domination that double consciousness was introduced to illuminate. We conclude that while more intersectional and pluralistic accounts of double consciousness may be desirable, the project of expansion has moral limits. Identifying these limitations, we outline ways in which double consciousness—as a tool for conceptualizing the genealogy of structural anti-Blackness—remains valuable in the absence of ever-expanding revision. (shrink)

This is a collection of seventeen essays on learning, teaching, and the philosophy of education. A sequel to Hawkins's 'The Informed Vision' (1947), this new volume covers a wide range of topics, from generating the most basic student interest in the subject matter at hand to the specific challenges of teaching science and mathematics. In the title essay, Hawkins addresses widespread concerns over low literacy rates and the poor state of our educational system, questioning our limited understanding of (...) literacy as the ability to manipulate the printed word. Another essay explicates methods of inducing children toward certain types of learning, and then letting their spontaneous, natural urges toward self-education take over. In his concluding essay on human equality, Hawkins argues -- contrary to recent works such as Richard J Herrnstein and Charles Murray's 'The Bell Curve' -- that it is the relative poverty or wealth of our intellectual nurturing with respect to the cultural mainstream that accounts for differences in educational performance, no congenital inequalities. Moreover, he seeks to address exactly what sort of equivalence or equality -- preferably one that does not erase individual and cultural differences-we can and ought unqualifiedly to approve of and so seek to realise. Whatever the topic, Hawkins's essays draw upon a lifetime of teaching experience, illuminating the multiplicity of methods that should be used to educate our children. (shrink)

There are, broadly speaking, two kinds of knowledge—analytic and intuitive, explicit and tacit. Analytic knowledge is arrived at by logical deductive thinking, and is a sequential thought process in which each step can be explained and defended. Intuitive knowledge, in contrast, is frequently alogical or nonrational, and often involves nonconscious mental processes. Though intuitive ways of knowing are essential to both scientific research and scientific medicine, the culture of medicine celebrates only the analytic, evidentiary kind of knowledge, while eschewing intuition (...) as being “nonscientific.” The popularity and prevalence of what is known as evidence-based medicine reflects this bias in favor of the analytic and the explicit. Though the evidence-based approach has contributed greatly to standardizing medical care, favoring treatments for which there is evidence of effectiveness, it has limitations. An overreliance on evidence-based medicine is problematic, because this approach leaves out important factors in the actual practice of clinical medicine such as diagnosis, nonverbal cures provided by patients, and the way the doctor–patient relationship bears on patient management and compliance, and because it is not appropriate for dealing with medical conditions that do not lend themselves to study by controlled clinical trials. (shrink)

Big Ideas for Little Kids includes everything a teacher, a parent, or a college student needs to teach philosophy to elementary school children from picture books. Written in a clear and accessible style, the book explains why it is important to allow young children access to philosophy during primary-school education. Wartenberg also gives advice on how to construct a "learner-centered" classroom, in which children discuss philosophical issues with one another as they respond to open-ended questions by saying whether they agree (...) or disagree with what others have said. (shrink)

There is an enduring and widespread perception amongst policy makers and practitioners that certain groups of children, in particular those who find learning difficult, have a detrimental effect on the achievement of other children. Challenging this basic assumption, this award-winning book argues that high levels of inclusion can be entirely compatible with high levels of achievement and that combining the two is not only possible but essential if all children are to have the opportunity to participate fully in education. This (...) fully revised second edition is packed with vivid case studies that explore the benefits and tensions for children and schools, and sets out to answer the following questions: What is the nature of the relationship between the inclusion of some children and the achievement of all? Are there strategies which can raise the achievement of all children, whilst safeguarding the inclusion of others who are more vulnerable? What changes can a school make to ensure high levels of inclusion as well as high levels of achievement for all its children? Achievement and Inclusion in Schools offers a fully up-to-date analysis of current issues in light of recent changes to education policy in England, Scotland, Wales and Northern Ireland. It provides practical guidance for practitioners and policy-makers, and will be of interest to anyone passionate about inclusive education. (shrink)

This chapter explores radical personal change and its relationship to well-being, welfare, or prudential value. Many theorists of welfare are committed to what is here called the future-based reasons view (FBR), which holds (1) that the best prudential choice in a situation is determined by which possible future has the greatest net welfare value for the subject and (2) what determines facts about future welfare are facts about the subject and the world at that future time. Although some cases of (...) radical change are intuitively prudentially good, many cases of really radical change are not. Yet FBR has trouble explaining this. Many people instinctively reach for the notion of identity to solve this problem—arguing that really radical change cannot be good because it alters who someone is. Yet, as the chapter argues, there are reasons to doubt that appeals to identity are appropriate. The chapter ends with the suggestion that prudential facts may explain why and when retaining identity matters, rather than the other way around, and points to a possible way forward for a theorist of welfare committed to FBR. (shrink)

v. 1. Editorial introduction -- v. 2. The English and Latin texts (i) -- v. 3. The English and Latin texts (ii).

This article is a contribution to our understanding of how Archilochean poetics may be situated in the longer poetic tradition. In examining two fragments that have received little attention, I hope to illustrate how Archilochus’ poetry both engaged with its predecessors and was in turn engaged by its successors. Fragment 222W employs a theme that was perhaps already conventional for Hesiod, in which the incompatibility of the sexes is implicated in the cycle of seasons, an idea that also seems relevant (...) to Archilochus’ quarrel with the daughters of Lycambes. Light is shed on 39W by comparing it to later words for skinning that serve as metaphors for cheating someone, the best known example of which is found in Catullus. In the first fragment the text can be elucidated by a look to Archilochus’ forerunners, and in the second by looking to his heirs. (shrink)

Frege believes that the content of declarative sentences divides into a thought and its ‘colouring’, perhaps combined with assertoric force. He further thinks it is important to separate the thought from its colouring. To do this, a criterion which determines sameness of sense between sentences must be deployed. But Frege provides three criteria for this task, each of which adjudicate on different grounds. In this article, rather than expand on criticisms levelled at two of the criteria offered, the author focuses (...) on the most promising candidate. As it stands, this criterion has problems, but not insuperable ones. He suggests an adjusted criterion that relies on the epistemic notion of triviality. He recommends this criterion as both harmonious with Frege’s broader thought and preferable to alternatives offered. The moral is that Frege individuates thoughts by deploying an epistemic concept, and this is the only suitable way for him to do so. (shrink)

What is the best way to account for the badness of pain and what sort of theory of welfare is best suited to accommodate this view? I argue that unpleasant sensory experiences are prudentially bad in the absence of contrary attitudes, but good when the object of positive attitudes. Pain is bad unless it is liked, enjoyed, valued etc. Interestingly, this view is incompatible with either pure objectivist or pure subjectivist understandings of welfare. However, there is a kind of welfare (...) theory that can incorporate this view of the badness of pain and which is very, very close to being a form of subjectivism. Moreover, this hybrid account of welfare is entirely compatible with the deep motivations of subjectivism. I therefore argue that those who lean towards welfare subjectivism should adopt this account of pain, and that we should revise our understanding of subjectivism to count such theories as subjective. (shrink)

In this book, T. M. Scanlon offers new answers to these questions, as they apply to the central part of morality that concerns what we owe to each other.

The past 15 years have witnessed an increasing interest in the comparative study of language and music as cognitive systems. This book presents an interdisciplinary study of language and music, exploring the following core areas - structural comparisons, evolution, learning and processing, and neuroscience.

This paper is an exposition and evaluation of the Agustín Rayo's views about the epistemology and metaphysics of mathematics, as they are presented in his book The Construction of Logical Space.